M621893 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	47.7798	70.1493%	1275000	40800000	0.0755	5.9359%	47.8553	71.9212%	1.7719%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	220000	0.0004	20.5994%	0.0004	60.2997%	10.2997%
GPU72	2⁴⁴	0.0000	54.5455%	11000	360000	0.0007	15.6187%	0.0007	61.6449%	7.0994%
Difference	+23	+47.7798	+15.6038%	+1264000	+40440000	+0.0749	-9.6828%	+47.8547	+10.2763%	+10.2763%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
621893	198873496542970818665753	24	77.396	159893660599951132 2² × 2111 × 18935772216953	2014-03-30	2111	18935772216953	91,959	22,730	42,453

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-31T00:00:00	Alex Kruppa	v4_computers	2000	40000		-		-	-	8.96776e-5	-	-	0.110%
2001-01-14T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.582%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.212%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.827%
2002-09-29T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.583%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.466%
2011-07-10T12:45:00	Jocelyn Larouche	Manual testing	369019	369019		-		-	-	0.008	-	-	1.474%
2011-08-31T00:06:00	Jocelyn Larouche	Manual testing	615032	615032		-		-	-	0.014	-	-	1.855%
2012-06-19T02:41:00	Jocelyn Larouche	Manual testing	621937	621937		-		-	-	0.014	-	-	1.864%
2012-08-01T01:16:00	Jocelyn Larouche	Manual testing	1243786	1243786		-		-	-	0.027	-	-	2.464%
2013-10-20T13:06:00	David Campeau	i5-2500k	1275000	40800000		-		-	-	0.076	-	-	5.936%
2016-03-17T18:49:51	alpertron	Manual testing	1000000	30000000	12	-		-	-	0.057	-	-	5.483%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.015	-	-
2001-10-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.031	-	-
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.062	-	-
2008-10-10T22:23:00	Sturle Sunde	bach.ifi	2⁵⁸	2⁵⁹		-	-	0.062	-	-
2008-10-10T23:07:00	Sturle Sunde	bach.ifi	2⁵⁹	2⁶⁰		-	-	0.123	-	-
2011-01-02T22:12:00	Sid & Andy	Toy_Soldier	2⁶⁰	2⁶¹		-	-	0.247	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.460 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	8.460 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.634	0.000%
25	50000	1.341	26.168%
30	250000	0.107	89.841%
35	1000000	0.007	99.298%

ECM Summary

B1	B2	factor	curves	GHz-days
		198873496542970818665753	1	0.00000e+0
50000	5000000		278	4.723
250000	25000000		44	3.738

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-24T11:58:00	Chad Davis	Bayes	50000	5000000						1	0.017
2007-10-20T06:23:00	James Heinrich	WHS	50000	5000000						1	0.017
2008-01-20T16:43:00	Steve Scott	Abit-3	50000	5000000						3	0.051
2008-09-12T23:55:00	Sturle Sunde	v23	50000	5000000						3	0.051
2008-11-23T19:28:00	Sturle Sunde	v21	50000	5000000						3	0.051
2009-02-09T19:44:00	Sturle Sunde	v17	50000	5000000						3	0.051
2009-03-29T00:56:00	Sturle Sunde	v21	50000	5000000						3	0.051
2009-06-26T01:15:00	Sturle Sunde	FLB-ST-0034	50000	5000000						3	0.051
2009-07-09T21:51:00	Architects Cubed	m1_06	50000	5000000						3	0.051
2009-08-18T21:52:00	linded	KCPB8P0-NET214	50000	5000000						3	0.051
2009-09-24T17:32:00	Sturle Sunde	PRE6S33KN9ZE3B5	50000	5000000						3	0.051
2009-10-21T23:35:00	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.051
2009-11-08T04:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-12-01T08:15:00	NeedGem Liou	PC133-Nettop	50000	5000000						3	0.051
2009-12-23T23:57:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-01-14T23:10:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-01-31T03:14:00	James Hintz	09_122109	50000	5000000						3	0.051
2010-02-15T06:18:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-03-10T22:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-03-28T21:21:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-04-25T07:57:00	James Hintz	17_012210	50000	5000000						3	0.051
2010-05-05T05:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-05-24T21:57:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-06-16T02:04:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-07-15T02:18:00	Sturle Sunde	PRE6S32KN9Z73F9	50000	5000000						3	0.051
2010-08-12T02:48:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-09-03T23:29:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-09-21T14:03:00	sannerud.com	Jim2010	50000	5000000						3	0.051
2010-10-09T23:54:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-10-24T20:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-11-09T04:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-11-29T19:53:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-12-12T00:25:00	Sturle Sunde	PRECZC44710WB	50000	5000000						3	0.051
2011-01-03T05:31:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-01-16T06:00:00	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.051
2011-01-30T18:28:00	Damian Silvestre	PcMa	50000	5000000						3	0.051
2011-02-16T22:11:00	Sturle Sunde	FLB-ST-0034	50000	5000000						3	0.051
2011-03-03T19:05:00	James Hintz	06_122109	50000	5000000						3	0.051
2011-03-15T02:49:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-03-30T23:04:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-04-22T22:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-05-18T23:06:00	Lukasz Wrobel	w-l	50000	5000000						3	0.051
2011-05-30T14:31:00	Lukasz Wrobel	w-l	50000	5000000						3	0.051
2011-06-19T03:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-07-16T11:49:00	Netanias	NCS2009Fermat	50000	5000000						3	0.051
2011-08-15T22:44:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-10-07T03:18:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-12-06T22:48:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.051
2012-02-04T05:21:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2012-03-17T00:35:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2012-06-04T03:03:00	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.051
2012-08-27T00:38:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2013-02-09T02:29:00	Lukasz Wrobel	v7	50000	5000000						3	0.051
2013-09-26T22:42:00	lopper	Surface_staples	50000	5000000						3	0.051
2013-12-13T13:31:00	Bruce	bfc-ws	50000	5000000						3	0.051
2014-03-30T07:37:00	Bruce	snowflake			198873496542970818665753	77.396		1		1	-
2016-05-06T13:28:43	TJAOI	Manual testing	50000	5000000						26	0.442
2017-02-10T18:27:38	TJAOI	Manual testing	50000	5000000						91	1.546
2019-12-16T13:23:44	TJAOI	Manual testing	250000	25000000						44	3.738

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1275000, B2 = 40800000 (P-1 stage 2)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1275000 (P-1 stage 1)

B1 = 1243786 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 621937 (P-1 stage 1)

B1 = 615032 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 369019 (P-1 stage 1)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 40000 (P-1 stage 2)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront